The production function for a product is given by q = 10 K1/2L1/2 where K is capital, and L is labor and q is output. a) Find the marginal product of labor and the marginal product of capital. b) Find the marginal rate of technical substitution between labor and capital. c) Denote the wage of labor by w and the rental of capital by What is the cost minimization condition for a firm? Show it diagrammatically. d) Now suppose w =30 and r = 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) e) Now suppose that the firm is in the short run and cannot vary the amount of capital. That is, it must use the same amount of capital as in part d. However, the firm wants to produce 1200 units of output. How much labor should it use to minimize its cost and what is the minimum cost of producing q =1200?
The production function for a product is given by q = 10 K1/2L1/2 where K is capital, and L is labor and q is output.
a) Find the marginal product of labor and the marginal product of capital.
b) Find the
c) Denote the wage of labor by w and the rental of capital by What is the cost minimization condition for a firm? Show it diagrammatically.
d) Now suppose w =30 and r = 120. What is the minimum cost of producing q=1000.
(You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.)
e) Now suppose that the firm is in the short run and cannot vary the amount of capital. That is, it must use the same amount of capital as in part d. However, the firm wants to produce 1200 units of output. How much labor should it use to minimize its cost and what is the minimum cost of producing q =1200?
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